
Associative Functions: Triangular Norms And Copulas
TRIANGULAR NORMS AND COPULAS
World Scientific Publishing Co Pte Ltd
Published on 23. February 2006
Book
Hardback
252 pages
978-981-256-671-3 (ISBN)
Description
The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the "triangular norms" introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis.This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.
Reviews / Votes
"This well-written and very readable book is probably quite unique: its main subject is a single functional equation, that of associativity (joined by some more or less related equations) and several of its equations."Zentralblatt MATHMore details
Language
English
Place of publication
Singapore
Singapore
Target group
College/higher education
Professional and scholarly
Product notice
sewn/stitched
Paper over boards
Dimensions
Height: 232 mm
Width: 158 mm
Thickness: 23 mm
Weight
570 gr
ISBN-13
978-981-256-671-3 (9789812566713)
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Schweitzer Classification
Persons
Author
Univ Politecnica De Catalunya, Spain
Illinois Inst Of Tech, Chicago, Usa
Univ Of Massachusetts, Usa